I have a set of alpha numeric displays from Sparkfun, the 1.0" Single Digit Alphanumeric Display - Blue - COM-09933 - SparkFun Electronics, and want to use a few of 74HC595 I have on hand. Most of the time I use the 74HC595's on displays with a common cathode, but this little display uses a common anode.
Is there a way to connect this display up using the 74HC595 to to a device with a common anode?
Would this work? 
Sorry about the oversize image.
Can't open the image, but using HC595 with current limiting resistors to sink current from individual cathodes is fine.
For brighter output, use TPIC6B595 to sink current instead, can do full 20mA on each segment without worry, vs being limited to 8-9mA per segment due to HC595 70mA total current limit.
With HC595, shifting 0 in will turn a segment on.
With 6B595, shift a 1 in turns the output on to go low and turn a segment on.
Looks like you are on the right track. A Google of:
74hc595 common anode
... offers up some ideas.
That display has dual blue serial LEDs per segment and needs more than 5V to turn them on.
Thus Vs = 7.5V or 9V on the common anode, needs current limiting resistors, and TPIC6B595 to sink current thru it.
Forward Voltage Vf Per Seg. : 6.4V typical, 7.6V max
Forward Voltage Vf Per Dot : 3.2V typical, 3.8V max
need different resistors for dots than segments.
(Vs - Vf)/.02 = resistor
Also need A1/A2 wired in parallel with a resistor each, D1/D2 wired in parallel with a resistor each, and G1/G2 wired in parallel with a resistor each.
Typically the data you send out will be:
0bdpGFEDCBA
and wire up the shift register to match:
Q7 dp
Q6 G
Q5 F
Q4 E
Q3 D
Q2 C
Q1 B
Q0 A